Thus, if the number of rows of \(S\)  is less than \(d\) , we obtain a dimension reduction for \(\Vert \cdot \Vert _{1,2}\)  subspace approximation.

[1]} give the following sufficient conditions for a distribution of matrices to be an \(\epsilon \) -lopsided embedding for \((A,B)\) . For the sake of completeness we reproduce their proof here.
